Sketching Quadratic Graphs from Roots and the Turning Point · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Sketching quadratic graphs from roots and the turning point

Mathematics · Algebra · ages 15-16
Name ______________________   Date ____________

  1. In the form (x + 3) squared + 2, what are the coordinates of the turning point?

    • (3, 2)
    • (3, -2)
    • (-3, -2)
    • (-3, 2)

  2. In the form (x - 4) squared - 7, what is the x-coordinate of the turning point?

    Answer: ______________

  3. A parabola has symmetry axis x = 5 and contains (2, 11). What is the x-coordinate of this point's reflected partner?

    Answer: ______________

  4. Which sketch feature is a line rather than a point?

    • The y-intercept (0, -8)
    • The symmetry axis x = -4
    • The turning point (-4, 6)
    • The x-intercept (-7, 0)

  5. For y = (x - 7)² - 16, the roots x = 3 and x = 11 belong to the intervals where y > 0.

    Circle one:   True   False

  6. For y = -x² + 10x - 21, the positive interval is 3 < x < b. What is its excluded upper boundary b?

    Answer: ______________

  7. The curve y = (x - 1) squared - 4 crosses the x-axis at which pair of x values?

    • 1 and 4
    • -1 and -3
    • 3 and 1
    • 3 and -1

  8. For y = -x² + 6x - 5, which x-values give y > 0?

    • x < 1 or x > 5
    • 1 < x < 5
    • x > 5 only
    • x < 1 only

  9. What is the y-coordinate of the maximum of y = -2x squared + 8x - 3?

    Answer: ______________

  10. A curve in the form y = (x - a) squared + b crosses the x-axis at 2 and 6. What is a?

    • 4
    • -4
    • 2
    • 6
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Answer key

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Sketching quadratic graphs from roots and the turning point W1-mt_RcrJIbbN2x-s1

  1. (-3, 2) · In (x + p) squared + q the turning point is (-p, q), so here it is (-3, 2).
  2. 4 · In (x + p) squared + q the turning point x-coordinate is -p. Here p is -4, so -p is 4.
  3. 8 · The partner is equally far from x = 5 on the other side: 5 + 3 = 8.
  4. The symmetry axis x = -4 · x = -4 describes a vertical line. Each coordinate pair describes one point.
  5. False · At either root, y = 0. This upward parabola is positive for x < 3 or x > 11, excluding the roots.
  6. 7 · The roots are 3 and 7. The graph is above the axis for 3 < x < 7, so b = 7.
  7. 3 and -1 · At an x-axis crossing, y = 0, so (x - 1) squared = 4. This gives x - 1 = 2 or -2, hence x is 3 or -1.
  8. 1 < x < 5 · The graph opens downward and has roots 1 and 5. It is positive strictly between them; both roots have y = 0.
  9. 5 · Completing the square gives -2(x - 2) squared + 5, so the maximum is at (2, 5).
  10. 4 · The line of symmetry is halfway between the roots, at x = 4, and in (x - a) squared + b it is x = a.
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